Table 2. Hypotheses for the distribution of ARGs in the community.

Pr[z] = Pr[x]∙Pr[y]	Genus Richness	RA Genes∙Taxon-1
$\mathrm{\Sigma }\mathrm{\Sigma }\frac{e^{-\lambda }{\lambda }^x}{x!}.\left(\genfrac{}{}{0pt}{}{n}{y}\right)p^y{\left(1-p\right)}^{n-y}$	$\frac{mean}{var}\approx 1$	p constant
$\mathrm{\Sigma }\mathrm{\Sigma }\frac{r(k+x)}{r\left(k\right)x!}\bullet {\left(\frac{k}{K+\mu }\right)}^k\bullet {\left(\frac{\mu }{K+\mu }\right)}^x\bullet \left(\genfrac{}{}{0pt}{}{N}{y}\right)p^y{(1-p)}^{N-y}$	$\frac{mean}{var}>1$	p constant
$\mathrm{\Sigma }\mathrm{\Sigma }\frac{e^{-\lambda }{\lambda }^x}{x!}\bullet \frac{\mathrm{\Gamma }(a+b)\bullet \mathrm{\Gamma }(y+a)\bullet \mathrm{\Gamma }(N-y+b)\bullet N!}{\mathrm{\Gamma }\left(a\right)\bullet \mathrm{\Gamma }\left(b\right)\bullet (N+a+b)\bullet \left(N-y\right)!\bullet y!}$	$\frac{mean}{var}\approx 1$	P variable
$\mathrm{\Sigma }\mathrm{\Sigma }\frac{\mathrm{\Gamma }(\kappa +x)}{\mathrm{\Gamma }\left(\kappa \right)x!}\bullet {\left(\frac{k}{k+\mu }\right)}^k\bullet {\left(\frac{\mu }{k+\mu }\right)}^x\bullet \frac{\mathrm{\Gamma }(a+b)\bullet \mathrm{\Gamma }(y+a)\bullet \mathrm{\Gamma }(N-y+b)\bullet N!}{\mathrm{\Gamma }\left(a\right)\bullet \mathrm{\Gamma }\left(b\right)\bullet \mathrm{\Gamma }(N+a+b)\bullet \left(N-y\right)!\bullet y!}$	$\frac{mean}{var}>1$	p variable